Question

The square of the sum of a number and six is eighty-one. find the number

Answer 1

Hi there! The numbers can be either -15 or 3.

Let the number be represented by X.
$(x + 6) {}^{2} = 81$

First we work out the parentheses.
${x}^{2} + 12x + 36 = 81$

Now subtract 81 from both sides.
${x}^{2} + 12x - 45 = 0$

Using the sum of 12 and a product of 45 we get.
$(x + 15)(x - 3) = 0$

AB = 0 gives A = 0 or B = 0
$x + 15 = 0 \: \: or \: \: x - 3 = 0$
$x = - 15 \: \: or \: \: x = 3$

Therefore, the numbers are either -15 or 3.